Staples seem to be widely interchangeable among stapler brands, in terms of the compatibility that is listed on the box, but brad nails are more specific.

If we are to believe the packaging, Arrow BN1810 nails (5/8", 18 gauge) can only be used in a few Arrow guns, whereas a Stanley TR250 calls specifically for model SWKBN625 brads: also 5/8" long, 18 gauge.

How different are these, and are they really not interchangeable? Do they have some key dimensions that are different?